Fundamental groups of rationally connected varieties

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Let U be an open subset of a unirational variety. We prove that there is rational curve C in U such that the fundamental group of C surjects onto the fundamental group of U. As a consequence we obtain new proofs of the theorems of Harbater and Colliot-Thélène on Galois covers and torsors over the p-adic line. We also obtain examples of pencils of curves of genus <14 whose monodromy group is the full Teichmüller group.
12 pages, LaTeX

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Algebraic Geometry, 14J45 (Primary) 14E20, 14F35, 14H15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/58886

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0003138
 http://arxiv.org/abs/math/0003138

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arXiv